Distillation of entanglement by projection on permutationally invariant subspaces

We consider distillation of entanglement from two-qubit states which are mixtures of two pure entangled states and one pure product state, which is orthogonal to them. We distill entanglement from such states by projecting n copies of the state on a permutationally invariant subspace and then applyi...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-03, Vol.45 (12), p.125303-26
Main Authors: Czechlewski, Miko aj, Grudka, Andrzej, Horodecki, Micha, Mozrzymas, Marek, Studzi ski, Micha
Format: Article
Language:English
Subjects:
Distillation
Entanglement
Equivalence
Exact sciences and technology
Exact solutions
Invariants
Mathematical analysis
Matrices (mathematics)
Matrix methods
Physics
Subspaces
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Summary:We consider distillation of entanglement from two-qubit states which are mixtures of two pure entangled states and one pure product state, which is orthogonal to them. We distill entanglement from such states by projecting n copies of the state on a permutationally invariant subspace and then applying one-way hashing protocol. We find analytical expressions for the rate of the protocol and show that for wide range of parameters, this protocol achieves higher rates than previous ones. We also generalize this method to higher-dimensional systems. To get analytical expression for two-qubit case, we faced a mathematical problem of diagonalizing a family of matrices enjoying some symmetries w.r.t. the symmetric group. We have solved this problem in two ways: (i) directly by the use of Schur-Weyl decomposition and Young symmetrizers and (ii) showing that the problem is equivalent to a problem of diagonalizing adjacency matrices in a particular instance of a so-called algebraic association scheme.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/12/125303